Images of hairy Reissner-Nordstr\'{o}m black hole illuminated by static accretions

We investigate the shadow and optical appearance of the hairy Reissner-Nordstr\"{o}m (RN) black hole illuminated by two toy models of static accretion. The hairy RN black hole was constructed in the gravitation decoupling approach to describe the deformation of a Schwarzschild black hole due to the inclusion of additional arbitrary source (scalar field, tensor field, fluidlike dark matter, etc). So it is characterized by the parameters: mass ($M$), deformation factor ($\alpha$), electric charge ($Q$) and the additional hairy charge ($l_o$), differentiating from the case in RN black hole. Though the specific background theory that results in this hairy RN black hole is still tricky, here we shall focus on the novel observable features introduced by the hair of this black hole. First, we find that for the hairy RN black hole, the event horizon, radius of photon sphere and critical impact parameter all increase as the increasings of $Q$ and $l_o$, but decrease as $\alpha$ grows. The three characterized parameters are found to have significant effects on the photon trajectories, shadows and images of hairy RN black hole surrounded by the static accretion disk and spherical accretion, respectively. Particularly, both $Q$ and $l_o$ have mutually reinforcing effects on the optical appearance and shadows of the hairy RN black hole, which implies that we may not distinguish the electric charge and hairy charge from the shadow and image of black hole in this scenario. Additionally, because of the competing effects of the charge parameters ($Q, l_o$) and the deviation parameter $\alpha$ on the observed intensities of brightness, the optical appearance between the hairy RN black hole and RN black hole could have degeneracies, indicating the indistinguishability. Our current results contribute more to the phenomenal aspects which could be helpful to build the background theory of hairy RN black hole.
Comment: 15 pages, 6 figures